Geometric Diagrams

Students often tend to think that geometric proofs are about diagrams when they are actually about the implications of relationships that a diagram merely illustrates. This activity is to drive home the point that a diagram cannot be used to infer the relationships it is meant to illustrate -- it could illustrate many different relationships. It is also meant to convey that any set of relationships could be illustrated by many different diagrams.

For each of Diagrams 1-3, provide two different sets of given relationships that are consistent with the diagram. By "consistent" I mean that the diagram would be a valid one to draw to illustrate the conditions you give. Then state the implications of the different sets of conditions for how the diagram would behave were you to vary something in it.

Remember that the point is to provide conditions consistent with the diagram, not to to give instructions for reproducing the diagram.

Diagram 1.
Your statements of given conditions:

Given conditions	Given conditions 2	Implications of different conditions for how diagram behaves were you to vary something in it

Diagram 2.

Diagram 3.